Low-dimensional embeddings of knowledge graphs and behavior graphs have proved remarkably powerful in varieties of tasks, from predicting unobserved edges between entities to content recommendation. The two types of graphs can contain distinct and complementary information for the same entities/nodes. However, previous works focus either on knowledge graph embedding or behavior graph embedding while few works consider both in a unified way. Here we present BEM , a Bayesian framework that incorporates the information from knowledge graphs and behavior graphs. To be more specific, BEM takes as prior the pre-trained embeddings from the knowledge graph, and integrates them with the pre-trained embeddings from the behavior graphs via a Bayesian generative model. BEM is able to mutually refine the embeddings from both sides while preserving their own topological structures. To show the superiority of our method, we conduct a range of experiments on three benchmark datasets: node classification, link prediction, triplet classification on two small datasets related to Freebase, and item recommendation on a large-scale e-commerce dataset.

A widely applicable Bayesian information criterion (Watanabe, 2013) is applicable for both regular and singular models in the model selection problem. This criterion tends to overestimate the log marginal likelihood. We identify an overestimating term of a widely applicable Bayesian information criterion. Adjustment of the term gives an asymptotically unbiased estimator of the leading two terms of asymptotic expansion of the log marginal likelihood. In numerical experiments on regular and singular models, the adjustment resulted in smaller bias than the original criterion.

Evidence in probabilistic reasoning may be ‘hard’ or ‘soft’, that is, it may be of yes/no form, or it may involve a strength of belief, in the unit interval [0, 1]. Reasoning with soft, [0, 1]-valued evidence is important in many situations but may lead to different, confusing interpretations. This paper intends to bring more mathematical and conceptual clarity to the field by shifting the existing focus from specification of soft evidence to accomodation of soft evidence. There are two main approaches, known as Jeffrey’s rule and Pearl’s method; they give different outcomes on soft evidence. This paper argues that they can be understood as correction and as improvement. It describes these two approaches as different ways of updating with soft evidence, highlighting their differences, similarities and applications. This account is based on a novel channel-based approach to Bayesian probability. Proper understanding of these two update mechanisms is highly relevant for inference, decision tools and probabilistic programming languages.

Deep neural network (DNN) regression models are widely used in applications requiring state-of-the-art predictive accuracy. However, until recently there has been little work on accurate uncertainty quantification for predictions from such models. We add to this literature by outlining an approach to constructing predictive distributions that are `marginally calibrated'. This is where the long run average of the predictive distributions of the response variable matches the observed empirical margin. Our approach considers a DNN regression with a conditionally Gaussian prior for the final layer weights, from which an implicit copula process on the feature space is extracted. This copula process is combined with a non-parametrically estimated marginal distribution for the response. The end result is a scalable distributional DNN regression method with marginally calibrated predictions, and our work complements existing methods for probability calibration. The approach is first illustrated using two applications of dense layer feed-forward neural networks. However, our main motivating applications are in likelihood-free inference, where distributional deep regression is used to estimate marginal posterior distributions. In two complex ecological time series examples we employ the implicit copulas of convolutional networks, and show that marginal calibration results in improved uncertainty quantification. Our approach also avoids the need for manual specification of summary statistics, a requirement that is burdensome for users and typical of competing likelihood-free inference methods.

Semi-supervised learning is a setting in which one has labeled and unlabeled data available. In this survey we explore different types of theoretical results when one uses unlabeled data in classification and regression tasks. Most methods that use unlabeled data rely on certain assumptions about the data distribution. When those assumptions are not met in reality, including unlabeled data may actually decrease performance. Studying such methods, it therefore is particularly important to have an understanding of the underlying theory. In this review we gather results about the possible gains one can achieve when using semi-supervised learning as well as results about the limits of such methods. More precisely, this review collects the answers to the following questions: What are, in terms of improving supervised methods, the limits of semi-supervised learning? What are the assumptions of different methods? What can we achieve if the assumptions are true? Finally, we also discuss the biggest bottleneck of semi-supervised learning, namely the assumptions they make.

Blood glucose value prediction is an important task in diabetes management. While it is reported that glucose concentration is sensitive to social context such as mood, physical activity, stress, diet, alongside the influence of diabetes pathologies, we need more research on data and methodologies to incorporate and evaluate signals about such temporal context into prediction models. Person-generated data sources, such as actively contributed surveys as well as passively mined data from social media offer opportunity to capture such context, however the self-reported nature and sparsity of such data mean that such data are noisier and less specific than physiological measures such as blood glucose values themselves. Therefore, here we propose a Gaussian Process model to both address these data challenges and combine blood glucose and latent feature representations of contextual data for a novel multi-signal blood glucose prediction task. We find this approach outperforms common methods for multi-variate data, as well as using the blood glucose values in isolation. Given a robust evaluation across two blood glucose datasets with different forms of contextual information, we conclude that multi-signal Gaussian Processes can improve blood glucose prediction by using contextual information and may provide a significant shift in blood glucose prediction research and practice.

Although GAN-based methods have received many achievements in the last few years, they have not been such successful in generating discrete data. The most important challenge of these methods is the difficulty of passing the gradient from the discriminator to the generator when the generator outputs are discrete. Despite several attempts done to alleviate this problem, none of the existing GAN-based methods has improved the performance of text generation (using measures that evaluate both the quality and the diversity of generated samples) compared to a generative RNN that is simply trained by the maximum likelihood approach. In this paper, we propose a new framework for generating discrete data by an adversarial approach in which we do not need to pass the gradient to the generator. In the proposed method, the update of either the generator or the discriminator can be accomplished straightforwardly. Moreover, we leverage the discreteness of data to explicitly model the data distribution and ensure the normalization of the generated distribution and consequently the convergence properties of the proposed method. Experimental results generally show the superiority of the proposed DGSAN method compared to the other GAN-based approaches for generating discrete sequential data.

Submitted to the Annals of Applied Statistics SCALABLE MODELING OF SPATIOTEMPORAL DATA USING THE VARIATIONAL AUTOENCODER: AN APPLICATION IN GLAUCOMA By Samuel I. Berchuck, Felipe A. Medeiros and Sayan Mukherjee Duke University As big spatial data becomes increasingly prevalent, classical spatiotemporal (ST) methods often do not scale well. While methods have been developed to account for high-dimensional spatial objects, the setting where there are exceedingly large samples of spatial observations has had less attention. The variational autoencoder (V AE), an unsupervised generative model based on deep learning and approximate Bayesian inference, fills this void using a latent variable specification that is inferred jointly across the large number of samples. In this manuscript, we compare the performance of the V AE with a more classical ST method when analyzing longitudinal visual fields from a large cohort of patients in a prospective glaucoma study. Through simulation and a case study, we demonstrate that the V AE is a scalable method for analyzing ST data, when the goal is to obtain accurate predictions. R code to implement the V AE can be found on GitHub: https://github.com/berchuck/vaeST. 1. Introduction. As high-speed computing and medical imaging become increasingly inexpensive, massive amounts of data are generated that have to be analyzed and are often spatial in nature (Bearden and Thompson, 2017; Smith and Nichols, 2018). In the case of medical imaging, the number of patients that can be imaged has skyrocketed in recent years, allowing for studies that include images from many thousands of patients (Van Essen et al., 2013; Miller et al., 2016). The current spatial statistics literature focuses heavily on scalability in terms of the number of spatial locations (Banerjee, 2017), however largely ignores the setting where a joint model is needed for spatiotemporal (ST) data that are generated from a large cohort. Historically, learning an appropriate generating process in this setting was untenable, typically leading to simplifying assumptions, such as point-wise (PW) modeling of locations across time (Fitzke et al., 1996). In particular, generative models using deep learning have shown great promise in modeling complex distributions, p( x), for x x 1: M in some potentially high-dimensional space X . Sampling from X is often intractable, so instead generative modeling learns a distribution q (x) that can be sampled from and is close to p (x) (Doersch, 2016). As such, generative modeling can be viewed as an approximate method for performing inference in high-dimensional contexts, when there is an overwhelming availability of observations x . Generative modeling, and in particular the variational auto-encoder (V AE), are well-suited for modeling large cohorts of ST data, because they can characterize variability in a spatial data source through joint modeling (Kingma and Welling, 2013).

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely many training samples that will perform well on unseen test samples. This learning task is difficult even if all training and test samples are drawn from the same distribution---especially if the dimension of the uncertainty is large relative to the training sample size. Wasserstein distributionally robust optimization seeks data-driven decisions that perform well under the most adverse distribution within a certain Wasserstein distance from a nominal distribution constructed from the training samples. In this tutorial we will argue that this approach has many conceptual and computational benefits. Most prominently, the optimal decisions can often be computed by solving tractable convex optimization problems, and they enjoy rigorous out-of-sample and asymptotic consistency guarantees. We will also show that Wasserstein distributionally robust optimization has interesting ramifications for statistical learning and motivates new approaches for fundamental learning tasks such as classification, regression, maximum likelihood estimation or minimum mean square error estimation, among others.

In several reinforcement learning (RL) scenarios such as security settings, there may be adversaries trying to interfere with the reward generating process for their own benefit. We introduce Threatened Markov Decision Processes (TMDPs) as a framework to support an agent against potential opponents in a RL context. We also propose a level-k thinking scheme resulting in a novel learning approach to deal with TMDPs. After introducing our framework and deriving theoretical results, relevant empirical evidence is given via extensive experiments, showing the benefits of accounting for adversaries in RL while the agent learns